Feedback time-optimal control synthesis for flexible structures with damping

This paper addresses the problem of time-optimal control for a flexible structure with damping. It has the objective of designing a control law that is capable of driving a flexible link from an initial state to a final state in minimum time while suppressing any residual vibrations at the final state. The control input is assumed to be limited in magnitude, resulting in an on-off type of actuation. The dynamics of the flexible link are assumed to be sufficiently described by a fourth-order system of differential equations with one rigid body mode and one flexible mode. The closed-loop time-optimal control law is constructed using Gulko's strategy.